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, 2012, 192618

A Finite Element Study of Micropipette Aspiration of Single Cells: Effect of Compressibility

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A Finite Element Study of Micropipette Aspiration of Single Cells: Effect of Compressibility

Amirhossein Jafari Bidhendi et al. Comput Math Methods Med.

Abstract

Micropipette aspiration (MA) technique has been widely used to measure the viscoelastic properties of different cell types. Cells experience nonlinear large deformations during the aspiration procedure. Neo-Hookean viscohyperelastic (NHVH) incompressible and compressible models were used to simulate the creep behavior of cells in MA, particularly accounting for the effect of compressibility, bulk relaxation, and hardening phenomena under large strain. In order to find optimal material parameters, the models were fitted to the experimental data available for mesenchymal stem cells. Finally, through Neo-Hookean porohyperelastic (NHPH) material model for the cell, the influence of fluid flow on the aspiration length of the cell was studied. Based on the results, we suggest that the compressibility and bulk relaxation/fluid flow play a significant role in the deformation behavior of single cells and should be taken into account in the analysis of the mechanics of cells.

Figures

Figure 1
Figure 1
(a) Three-parameter viscoelastic linear solid for the cell and (b) infinite half-space model for the cell in MA.
Figure 2
Figure 2
(a) The axisymmetric FE mesh of micropipette aspiration. (b) NHPH model of micropipette aspiration simulating the fluid exchange and velocity in boundary of the cell.
Figure 3
Figure 3
Optimized compressible and incompressible NHVH models as well as incompressible NHVH with model inputs from the literature [5] based on the Sato et al. analytical solution.
Figure 4
Figure 4
The FE results for NHVH cell model with different values of Poisson's ratio (ν) without bulk relaxation (K = K 0). Other parameters were Prony shear relaxation parameter g̅p=0.51, time constant τ = 3.6 (s), initial shear modulus G 0 = 414 (Pa), and aspiration pressure P = 890 (Pa).
Figure 5
Figure 5
The FE results for NHVH cell model with different values of the Prony shear relaxation parameter g̅p. Other parameters were Prony bulk relaxation parameter k̅p=0, time constant τ = 3.6 (s), initial shear modulus G 0 = 414 (Pa), Poisson's ratio v = 0.42, and aspiration pressure of P = 890 (Pa).
Figure 6
Figure 6
The FE results for NHVH cell model for different values of the Prony bulk relaxation parameter k̅p. Other parameters were g̅p=0.4, time constant τ = 3.6 (s), initial shear modulus G 0 = 414 (Pa), Poisson's ratio v = 0.42, and aspiration pressure P = 890 (Pa).
Figure 7
Figure 7
The NHVH FE model results for different values of Prony shear relaxation parameter, g̅p, and Prony bulk relaxation parameter, k̅p, with different Poisson's ratios: (a) v = 0.3 and (b) v = 0.4. Other parameters were time constant τ = 3.6 (s), initial shear modulus G 0 = 414 (Pa), and aspiration pressure P = 890 (Pa). In this figure, the initial elastic jumps have been removed.

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References

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